Suggested languages for you:

Americas

Europe

Q3.

Expert-verified
Found in: Page 302

Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

Solve each inequality. Then graph it on a number line.$p-4<-7$

The required value of x is $\left(-\infty ,-3\right)$. The graph on the number line is,

See the step by step solution

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{or}\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$1.\text{}b\le c⇒b±a\le c±a\phantom{\rule{0ex}{0ex}}2.\text{}b\le c⇒ab\le ac,\text{if}a>0\phantom{\rule{0ex}{0ex}}3.\text{}b\le c⇒ab\ge ac,\text{if}a<0$

Step 2. Solve the inequality for x.

In order to solve the inequality:

$p-4<-7$

Add 4 both sides of the inequality, as

$p-4<-7\phantom{\rule{0ex}{0ex}}p-4+4<-7+4\phantom{\rule{0ex}{0ex}}p<-3$

Thus, the solution of the given inequality is every number is strictly less than $-3$, this can be represented in the interval form, as width="69" style="max-width: none; vertical-align: -4px;" $\left(-\infty ,-3\right)$.

Step 3. Plot the graph on the number line.

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point $-3$ is strict, so use a hollow circle at point $-3$. And the solution interval at left endpoint $-\infty$, thus every point strictly less than $-3$ is in the solution interval of given inequality. The graph of the solution of inequality is shown below:

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.